Tell me more ×
Cross Validated is a question and answer site for statisticians, data analysts, data miners and data visualization experts. It's 100% free, no registration required.
up vote 1 down vote favorite

Recent history suggests that one supplier fails to meet this new specification 20% of the time. Assume that the next 15 batches of this alloy are a random sample.

How can I find the expected number of shipments that do meet the new specifications, and the standard deviation?

share|improve this question
2  
This question needs more information. What do you mean by "20% of the time"? is it 20% of the batches given by 1 supplier are bad, or that 20% of suppliers give batches which are all bad? And does 1 supplier give only 1 batch - or can they give multiple batches? And what is the random sample of? is it of 15 batches from 1 shipment, or a random selection of 15 batches from multiple shipments? – probabilityislogic Apr 6 '11 at 13:28

1 Answer

up vote 3 down vote accepted

A simple approach would be to assume that each shipment will meet the specification with $p = 1 - 20\% = 80\%$ probability. The number of shipments meeting the specification (k) will then follow a binomial distribution: k ~ B(15, 80%) and the expected value will be $n \cdot p = 15 \cdot 80\%=12$. The standard error of this estimate is the standard deviation of the binomial distribution: $\sqrt{n p (1 − p)} = 1.55$, however, k is not normally distributed.

A more complicated approach would account for the fact that the 20% fail rate is only an estimate based on "recent history". So the actual fail rate may be somewhat lower or higher as well, and the above approach underestimates the uncertainty of the expected value. As we don't exactly know where the 20% came from, we can not calculate this.

share|improve this answer

Your Answer

 
discard

By posting your answer, you agree to the privacy policy and terms of service.